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<p>We investigate the dynamics of four-dimensional <InlineEquation ID="IEq2"> <EquationSource Format="MATHML"><math display="inline"> <mi mathvariant="script">N</mi> <mo>=</mo> <mn>2</mn> </math></EquationSource> <EquationSource Format="TEX">\( \mathcal{N}=2 \)</EquationSource> </InlineEquation> SU(2) super Yang-Mills theory on an AdS background. We propose that the boundary conditions that preserve the AdS super-isometries are determined by maximizing the real part of the AdS partition function <i>F</i><sub>AdS</sub> = −log <i>Z</i><sub>AdS</sub>. At weak coupling Λ<i>L</i> ≪ 1 the maximization singles out the Dirichlet boundary condition with an SU(2) boundary global symmetry, corresponding to the classical vacuum at the origin of the Coulomb branch with fully un-higgsed gauge group. We find that for Λ<i>L</i> ~ 𝒪(1) new boundary conditions are favored, with gauge-group higgsed down to U(1), matching the expectation from the flat space limit. We use supersymmetric localization to compute <i>Z</i><sub>AdS</sub> nonperturbatively. We further provide evidence for a relation between <i>F</i><sub>AdS</sub> and the <InlineEquation ID="IEq3"> <EquationSource Format="MATHML"><math display="inline"> <mi mathvariant="script">N</mi> <mo>=</mo> <mn>2</mn> </math></EquationSource> <EquationSource Format="TEX">\( \mathcal{N}=2 \)</EquationSource> </InlineEquation> prepotential in AdS background.</p>

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\( \mathcal{N}=2 \) super Yang-Mills in AdS4 and FAdS-maximization

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年3月27日

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  • Davide Bason,
  • Christian Copetti,
  • Lorenzo Di Pietro,
  • Ziming Ji

摘要

We investigate the dynamics of four-dimensional N = 2 \( \mathcal{N}=2 \) SU(2) super Yang-Mills theory on an AdS background. We propose that the boundary conditions that preserve the AdS super-isometries are determined by maximizing the real part of the AdS partition function FAdS = −log ZAdS. At weak coupling ΛL ≪ 1 the maximization singles out the Dirichlet boundary condition with an SU(2) boundary global symmetry, corresponding to the classical vacuum at the origin of the Coulomb branch with fully un-higgsed gauge group. We find that for ΛL ~ 𝒪(1) new boundary conditions are favored, with gauge-group higgsed down to U(1), matching the expectation from the flat space limit. We use supersymmetric localization to compute ZAdS nonperturbatively. We further provide evidence for a relation between FAdS and the N = 2 \( \mathcal{N}=2 \) prepotential in AdS background.